Concentration of conduction electrons

Use the given electrical resistivity and the formula for resistivity in terms of n and the mean relaxation time to calculate the mean relaxation time. Calculate the Fermi energy using the formula for Fermi energy in terms of n and the free electron mass. Calculate the Fermi velocity using the formula for Fermi velocity in terms of n and the free electron mass. Finally, use the Fermi velocity and mean relaxation time to calculate the mean free path at the Fermi level.In summary, to calculate the concentration of conduction electrons, you need to first calculate the free electron density using the given mass density and molar mass. Then, use the electrical resistivity and the formula for resistivity to calculate the mean relaxation time. From there,
  • #1
steph_mil
5
0
This is part of a longer problem, and probably obvious, but if I calculate this wrong, the rest of the calculations will be wrong too!...

Question: Given the mass density, molar mass, and electrical resistivity of a substance at room temperature, how do you calculate the concentration of the conduction electrons assuming the effective mass is equal to the free electron mass?

(Perhaps the electrical resistivity is not necessary to answer this part of the problem?)

The rest of the problem asks for mean relaxation time, fermi energy, fermi velocity, and mean free path at the fermi level. I know how to solve for these once I can calculate the concentration of conduction electrons, so I am not completely helpless, but I just can't get the problem started.

Thank you!
 
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  • #2
Calculate no. of atoms electrons per unit volume using the given mass density and molar mass.
You probably need to assume that each atom contributes one free electron, since free electrons are the ones responsible for conduction.So you now have the free electron density n(=concentration of atoms).
 

1. What is concentration of conduction electrons?

The concentration of conduction electrons refers to the number of free electrons within a material that are able to move and carry an electric current. This number is measured in units of per cubic meter (m-3) or per cubic centimeter (cm-3).

2. How is the concentration of conduction electrons determined?

The concentration of conduction electrons can be determined through various methods, such as Hall Effect measurements, resistivity measurements, or by using the band theory of solids. These methods involve measuring the electrical and magnetic properties of the material to determine the number of free electrons present.

3. What factors affect the concentration of conduction electrons?

The concentration of conduction electrons can be influenced by a variety of factors, including the type of material, temperature, impurities, and external electric or magnetic fields. Materials with a higher number of valence electrons, such as metals, tend to have a higher concentration of conduction electrons.

4. Why is the concentration of conduction electrons important?

The concentration of conduction electrons is important because it determines the conductivity and other electrical properties of a material. Materials with a higher concentration of conduction electrons are good conductors of electricity, while materials with a lower concentration are insulators. This property is crucial in many applications, such as in electronic devices and wiring.

5. How can the concentration of conduction electrons be altered or controlled?

The concentration of conduction electrons can be altered or controlled through various methods, such as doping with impurities, applying external electric or magnetic fields, or changing the temperature. These methods can either increase or decrease the number of free electrons in a material, thus affecting its electrical properties.

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